Highest Common Factor of 756, 990, 872, 149 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 756, 990, 872, 149 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 756, 990, 872, 149 is 1 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 756, 990, 872, 149 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 756, 990, 872, 149 is 1.
HCF(756, 990, 872, 149) = 1
HCF of 756, 990, 872, 149 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 756, 990, 872, 149 is 1.
Highest Common Factor of 756,990,872,149 is 1
Step 1: Since 990 > 756, we apply the division lemma to 990 and 756, to get
990 = 756 x 1 + 234
Step 2: Since the reminder 756 ≠ 0, we apply division lemma to 234 and 756, to get
756 = 234 x 3 + 54
Step 3: We consider the new divisor 234 and the new remainder 54, and apply the division lemma to get
234 = 54 x 4 + 18
We consider the new divisor 54 and the new remainder 18, and apply the division lemma to get
54 = 18 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 756 and 990 is 18
Notice that 18 = HCF(54,18) = HCF(234,54) = HCF(756,234) = HCF(990,756) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 872 > 18, we apply the division lemma to 872 and 18, to get
872 = 18 x 48 + 8
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 8 and 18, to get
18 = 8 x 2 + 2
Step 3: We consider the new divisor 8 and the new remainder 2, and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 18 and 872 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(872,18) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 149 > 2, we apply the division lemma to 149 and 2, to get
149 = 2 x 74 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 149 is 1
Notice that 1 = HCF(2,1) = HCF(149,2) .
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Frequently Asked Questions on HCF of 756, 990, 872, 149 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 756, 990, 872, 149?
Answer: HCF of 756, 990, 872, 149 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 756, 990, 872, 149 using Euclid's Algorithm?
Answer: For arbitrary numbers 756, 990, 872, 149 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.