Highest Common Factor of 632, 748, 172 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 632, 748, 172 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 632, 748, 172 is 4 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 632, 748, 172 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 632, 748, 172 is 4.
HCF(632, 748, 172) = 4
HCF of 632, 748, 172 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 632, 748, 172 is 4.
Highest Common Factor of 632,748,172 is 4
Step 1: Since 748 > 632, we apply the division lemma to 748 and 632, to get
748 = 632 x 1 + 116
Step 2: Since the reminder 632 ≠ 0, we apply division lemma to 116 and 632, to get
632 = 116 x 5 + 52
Step 3: We consider the new divisor 116 and the new remainder 52, and apply the division lemma to get
116 = 52 x 2 + 12
We consider the new divisor 52 and the new remainder 12,and apply the division lemma to get
52 = 12 x 4 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 632 and 748 is 4
Notice that 4 = HCF(12,4) = HCF(52,12) = HCF(116,52) = HCF(632,116) = HCF(748,632) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 172 > 4, we apply the division lemma to 172 and 4, to get
172 = 4 x 43 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 172 is 4
Notice that 4 = HCF(172,4) .
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Frequently Asked Questions on HCF of 632, 748, 172 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 632, 748, 172?
Answer: HCF of 632, 748, 172 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 632, 748, 172 using Euclid's Algorithm?
Answer: For arbitrary numbers 632, 748, 172 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.