Highest Common Factor of 752, 916 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 752, 916 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 752, 916 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 752, 916 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 752, 916 is 4.
HCF(752, 916) = 4
HCF of 752, 916 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 752, 916 is 4.
Highest Common Factor of 752,916 is 4
Step 1: Since 916 > 752, we apply the division lemma to 916 and 752, to get
916 = 752 x 1 + 164
Step 2: Since the reminder 752 ≠ 0, we apply division lemma to 164 and 752, to get
752 = 164 x 4 + 96
Step 3: We consider the new divisor 164 and the new remainder 96, and apply the division lemma to get
164 = 96 x 1 + 68
We consider the new divisor 96 and the new remainder 68,and apply the division lemma to get
96 = 68 x 1 + 28
We consider the new divisor 68 and the new remainder 28,and apply the division lemma to get
68 = 28 x 2 + 12
We consider the new divisor 28 and the new remainder 12,and apply the division lemma to get
28 = 12 x 2 + 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 752 and 916 is 4
Notice that 4 = HCF(12,4) = HCF(28,12) = HCF(68,28) = HCF(96,68) = HCF(164,96) = HCF(752,164) = HCF(916,752) .
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Frequently Asked Questions on HCF of 752, 916 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 752, 916?
Answer: HCF of 752, 916 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 752, 916 using Euclid's Algorithm?
Answer: For arbitrary numbers 752, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.