Highest Common Factor of 712, 2624 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 712, 2624 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 712, 2624 is 8 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 712, 2624 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 712, 2624 is 8.
HCF(712, 2624) = 8
HCF of 712, 2624 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 712, 2624 is 8.
Highest Common Factor of 712,2624 is 8
Step 1: Since 2624 > 712, we apply the division lemma to 2624 and 712, to get
2624 = 712 x 3 + 488
Step 2: Since the reminder 712 ≠ 0, we apply division lemma to 488 and 712, to get
712 = 488 x 1 + 224
Step 3: We consider the new divisor 488 and the new remainder 224, and apply the division lemma to get
488 = 224 x 2 + 40
We consider the new divisor 224 and the new remainder 40,and apply the division lemma to get
224 = 40 x 5 + 24
We consider the new divisor 40 and the new remainder 24,and apply the division lemma to get
40 = 24 x 1 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 712 and 2624 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(40,24) = HCF(224,40) = HCF(488,224) = HCF(712,488) = HCF(2624,712) .
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Frequently Asked Questions on HCF of 712, 2624 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 712, 2624?
Answer: HCF of 712, 2624 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 712, 2624 using Euclid's Algorithm?
Answer: For arbitrary numbers 712, 2624 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
