Highest Common Factor of 416, 992 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 416, 992 i.e. 32 the largest integer that leaves a remainder zero for all numbers.
HCF of 416, 992 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 416, 992 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 416, 992 is 32.
HCF(416, 992) = 32
HCF of 416, 992 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 416, 992 is 32.
Highest Common Factor of 416,992 is 32
Step 1: Since 992 > 416, we apply the division lemma to 992 and 416, to get
992 = 416 x 2 + 160
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 160 and 416, to get
416 = 160 x 2 + 96
Step 3: We consider the new divisor 160 and the new remainder 96, and apply the division lemma to get
160 = 96 x 1 + 64
We consider the new divisor 96 and the new remainder 64,and apply the division lemma to get
96 = 64 x 1 + 32
We consider the new divisor 64 and the new remainder 32,and apply the division lemma to get
64 = 32 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 416 and 992 is 32
Notice that 32 = HCF(64,32) = HCF(96,64) = HCF(160,96) = HCF(416,160) = HCF(992,416) .
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Frequently Asked Questions on HCF of 416, 992 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 416, 992?
Answer: HCF of 416, 992 is 32 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 416, 992 using Euclid's Algorithm?
Answer: For arbitrary numbers 416, 992 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.