Highest Common Factor of 123, 90, 735, 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 123, 90, 735, 177 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 123, 90, 735, 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 123, 90, 735, 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 123, 90, 735, 177 is 3.
HCF(123, 90, 735, 177) = 3
HCF of 123, 90, 735, 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 123, 90, 735, 177 is 3.
Highest Common Factor of 123,90,735,177 is 3
Step 1: Since 123 > 90, we apply the division lemma to 123 and 90, to get
123 = 90 x 1 + 33
Step 2: Since the reminder 90 ≠ 0, we apply division lemma to 33 and 90, to get
90 = 33 x 2 + 24
Step 3: We consider the new divisor 33 and the new remainder 24, and apply the division lemma to get
33 = 24 x 1 + 9
We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma 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 123 and 90 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(33,24) = HCF(90,33) = HCF(123,90) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 735 > 3, we apply the division lemma to 735 and 3, to get
735 = 3 x 245 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 735 is 3
Notice that 3 = HCF(735,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 177 > 3, we apply the division lemma to 177 and 3, to get
177 = 3 x 59 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 177 is 3
Notice that 3 = HCF(177,3) .
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Frequently Asked Questions on HCF of 123, 90, 735, 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 123, 90, 735, 177?
Answer: HCF of 123, 90, 735, 177 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 123, 90, 735, 177 using Euclid's Algorithm?
Answer: For arbitrary numbers 123, 90, 735, 177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.