Highest Common Factor of 640, 864 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 640, 864 i.e. 32 the largest integer that leaves a remainder zero for all numbers.
HCF of 640, 864 is 32 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 640, 864 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 640, 864 is 32.
HCF(640, 864) = 32
HCF of 640, 864 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 640, 864 is 32.
Highest Common Factor of 640,864 is 32
Step 1: Since 864 > 640, we apply the division lemma to 864 and 640, to get
864 = 640 x 1 + 224
Step 2: Since the reminder 640 ≠ 0, we apply division lemma to 224 and 640, to get
640 = 224 x 2 + 192
Step 3: We consider the new divisor 224 and the new remainder 192, and apply the division lemma to get
224 = 192 x 1 + 32
We consider the new divisor 192 and the new remainder 32, and apply the division lemma to get
192 = 32 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 640 and 864 is 32
Notice that 32 = HCF(192,32) = HCF(224,192) = HCF(640,224) = HCF(864,640) .
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Frequently Asked Questions on HCF of 640, 864 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 640, 864?
Answer: HCF of 640, 864 is 32 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 640, 864 using Euclid's Algorithm?
Answer: For arbitrary numbers 640, 864 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.