Highest Common Factor of 656, 87664 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 656, 87664 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 656, 87664 is 16 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 656, 87664 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 656, 87664 is 16.
HCF(656, 87664) = 16
HCF of 656, 87664 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 656, 87664 is 16.
Highest Common Factor of 656,87664 is 16
Step 1: Since 87664 > 656, we apply the division lemma to 87664 and 656, to get
87664 = 656 x 133 + 416
Step 2: Since the reminder 656 ≠ 0, we apply division lemma to 416 and 656, to get
656 = 416 x 1 + 240
Step 3: We consider the new divisor 416 and the new remainder 240, and apply the division lemma to get
416 = 240 x 1 + 176
We consider the new divisor 240 and the new remainder 176,and apply the division lemma to get
240 = 176 x 1 + 64
We consider the new divisor 176 and the new remainder 64,and apply the division lemma to get
176 = 64 x 2 + 48
We consider the new divisor 64 and the new remainder 48,and apply the division lemma to get
64 = 48 x 1 + 16
We consider the new divisor 48 and the new remainder 16,and apply the division lemma to get
48 = 16 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 656 and 87664 is 16
Notice that 16 = HCF(48,16) = HCF(64,48) = HCF(176,64) = HCF(240,176) = HCF(416,240) = HCF(656,416) = HCF(87664,656) .
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Frequently Asked Questions on HCF of 656, 87664 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 656, 87664?
Answer: HCF of 656, 87664 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 656, 87664 using Euclid's Algorithm?
Answer: For arbitrary numbers 656, 87664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.