Highest Common Factor of 974, 416 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 974, 416 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 974, 416 is 2 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 974, 416 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 974, 416 is 2.
HCF(974, 416) = 2
HCF of 974, 416 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 974, 416 is 2.
Highest Common Factor of 974,416 is 2
Step 1: Since 974 > 416, we apply the division lemma to 974 and 416, to get
974 = 416 x 2 + 142
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 142 and 416, to get
416 = 142 x 2 + 132
Step 3: We consider the new divisor 142 and the new remainder 132, and apply the division lemma to get
142 = 132 x 1 + 10
We consider the new divisor 132 and the new remainder 10,and apply the division lemma to get
132 = 10 x 13 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 974 and 416 is 2
Notice that 2 = HCF(10,2) = HCF(132,10) = HCF(142,132) = HCF(416,142) = HCF(974,416) .
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Frequently Asked Questions on HCF of 974, 416 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 974, 416?
Answer: HCF of 974, 416 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 974, 416 using Euclid's Algorithm?
Answer: For arbitrary numbers 974, 416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.