Highest Common Factor of 672, 3762 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 672, 3762 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 672, 3762 is 6 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 672, 3762 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 672, 3762 is 6.
HCF(672, 3762) = 6
HCF of 672, 3762 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 672, 3762 is 6.
Highest Common Factor of 672,3762 is 6
Step 1: Since 3762 > 672, we apply the division lemma to 3762 and 672, to get
3762 = 672 x 5 + 402
Step 2: Since the reminder 672 ≠ 0, we apply division lemma to 402 and 672, to get
672 = 402 x 1 + 270
Step 3: We consider the new divisor 402 and the new remainder 270, and apply the division lemma to get
402 = 270 x 1 + 132
We consider the new divisor 270 and the new remainder 132,and apply the division lemma to get
270 = 132 x 2 + 6
We consider the new divisor 132 and the new remainder 6,and apply the division lemma to get
132 = 6 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 672 and 3762 is 6
Notice that 6 = HCF(132,6) = HCF(270,132) = HCF(402,270) = HCF(672,402) = HCF(3762,672) .
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Frequently Asked Questions on HCF of 672, 3762 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 672, 3762?
Answer: HCF of 672, 3762 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 672, 3762 using Euclid's Algorithm?
Answer: For arbitrary numbers 672, 3762 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.