Highest Common Factor of 990, 378, 300, 177 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 990, 378, 300, 177 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 990, 378, 300, 177 is 3 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 990, 378, 300, 177 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 990, 378, 300, 177 is 3.
HCF(990, 378, 300, 177) = 3
HCF of 990, 378, 300, 177 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 990, 378, 300, 177 is 3.
Highest Common Factor of 990,378,300,177 is 3
Step 1: Since 990 > 378, we apply the division lemma to 990 and 378, to get
990 = 378 x 2 + 234
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 234 and 378, to get
378 = 234 x 1 + 144
Step 3: We consider the new divisor 234 and the new remainder 144, and apply the division lemma to get
234 = 144 x 1 + 90
We consider the new divisor 144 and the new remainder 90,and apply the division lemma to get
144 = 90 x 1 + 54
We consider the new divisor 90 and the new remainder 54,and apply the division lemma to get
90 = 54 x 1 + 36
We consider the new divisor 54 and the new remainder 36,and apply the division lemma to get
54 = 36 x 1 + 18
We consider the new divisor 36 and the new remainder 18,and apply the division lemma to get
36 = 18 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 990 and 378 is 18
Notice that 18 = HCF(36,18) = HCF(54,36) = HCF(90,54) = HCF(144,90) = HCF(234,144) = HCF(378,234) = HCF(990,378) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 300 > 18, we apply the division lemma to 300 and 18, to get
300 = 18 x 16 + 12
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 12 and 18, to get
18 = 12 x 1 + 6
Step 3: We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 18 and 300 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(300,18) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 177 > 6, we apply the division lemma to 177 and 6, to get
177 = 6 x 29 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 177 is 3
Notice that 3 = HCF(6,3) = HCF(177,6) .
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Frequently Asked Questions on HCF of 990, 378, 300, 177 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 990, 378, 300, 177?
Answer: HCF of 990, 378, 300, 177 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 990, 378, 300, 177 using Euclid's Algorithm?
Answer: For arbitrary numbers 990, 378, 300, 177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.