Highest Common Factor of 7374, 977 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 7374, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7374, 977 is 1 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 7374, 977 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 7374, 977 is 1.
HCF(7374, 977) = 1
HCF of 7374, 977 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7374, 977 is 1.
Highest Common Factor of 7374,977 is 1
Step 1: Since 7374 > 977, we apply the division lemma to 7374 and 977, to get
7374 = 977 x 7 + 535
Step 2: Since the reminder 977 ≠ 0, we apply division lemma to 535 and 977, to get
977 = 535 x 1 + 442
Step 3: We consider the new divisor 535 and the new remainder 442, and apply the division lemma to get
535 = 442 x 1 + 93
We consider the new divisor 442 and the new remainder 93,and apply the division lemma to get
442 = 93 x 4 + 70
We consider the new divisor 93 and the new remainder 70,and apply the division lemma to get
93 = 70 x 1 + 23
We consider the new divisor 70 and the new remainder 23,and apply the division lemma to get
70 = 23 x 3 + 1
We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get
23 = 1 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7374 and 977 is 1
Notice that 1 = HCF(23,1) = HCF(70,23) = HCF(93,70) = HCF(442,93) = HCF(535,442) = HCF(977,535) = HCF(7374,977) .
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Frequently Asked Questions on HCF of 7374, 977 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 7374, 977?
Answer: HCF of 7374, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7374, 977 using Euclid's Algorithm?
Answer: For arbitrary numbers 7374, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.