Highest Common Factor of 928, 800, 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 928, 800, 916 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 928, 800, 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 928, 800, 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 928, 800, 916 is 4.
HCF(928, 800, 916) = 4
HCF of 928, 800, 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 928, 800, 916 is 4.
Highest Common Factor of 928,800,916 is 4
Step 1: Since 928 > 800, we apply the division lemma to 928 and 800, to get
928 = 800 x 1 + 128
Step 2: Since the reminder 800 ≠ 0, we apply division lemma to 128 and 800, to get
800 = 128 x 6 + 32
Step 3: We consider the new divisor 128 and the new remainder 32, and apply the division lemma to get
128 = 32 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 928 and 800 is 32
Notice that 32 = HCF(128,32) = HCF(800,128) = HCF(928,800) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 916 > 32, we apply the division lemma to 916 and 32, to get
916 = 32 x 28 + 20
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 20 and 32, to get
32 = 20 x 1 + 12
Step 3: We consider the new divisor 20 and the new remainder 12, and apply the division lemma to get
20 = 12 x 1 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 32 and 916 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(32,20) = HCF(916,32) .
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Frequently Asked Questions on HCF of 928, 800, 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 928, 800, 916?
Answer: HCF of 928, 800, 916 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 928, 800, 916 using Euclid's Algorithm?
Answer: For arbitrary numbers 928, 800, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.