Highest Common Factor of 977, 3700 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 977, 3700 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 977, 3700 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 977, 3700 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 977, 3700 is 1.
HCF(977, 3700) = 1
HCF of 977, 3700 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 977, 3700 is 1.
Highest Common Factor of 977,3700 is 1
Step 1: Since 3700 > 977, we apply the division lemma to 3700 and 977, to get
3700 = 977 x 3 + 769
Step 2: Since the reminder 977 ≠ 0, we apply division lemma to 769 and 977, to get
977 = 769 x 1 + 208
Step 3: We consider the new divisor 769 and the new remainder 208, and apply the division lemma to get
769 = 208 x 3 + 145
We consider the new divisor 208 and the new remainder 145,and apply the division lemma to get
208 = 145 x 1 + 63
We consider the new divisor 145 and the new remainder 63,and apply the division lemma to get
145 = 63 x 2 + 19
We consider the new divisor 63 and the new remainder 19,and apply the division lemma to get
63 = 19 x 3 + 6
We consider the new divisor 19 and the new remainder 6,and apply the division lemma to get
19 = 6 x 3 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 977 and 3700 is 1
Notice that 1 = HCF(6,1) = HCF(19,6) = HCF(63,19) = HCF(145,63) = HCF(208,145) = HCF(769,208) = HCF(977,769) = HCF(3700,977) .
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Frequently Asked Questions on HCF of 977, 3700 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 977, 3700?
Answer: HCF of 977, 3700 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 977, 3700 using Euclid's Algorithm?
Answer: For arbitrary numbers 977, 3700 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.