Highest Common Factor of 1337, 6972 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 1337, 6972 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 1337, 6972 is 7 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 1337, 6972 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 1337, 6972 is 7.
HCF(1337, 6972) = 7
HCF of 1337, 6972 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1337, 6972 is 7.
Highest Common Factor of 1337,6972 is 7
Step 1: Since 6972 > 1337, we apply the division lemma to 6972 and 1337, to get
6972 = 1337 x 5 + 287
Step 2: Since the reminder 1337 ≠ 0, we apply division lemma to 287 and 1337, to get
1337 = 287 x 4 + 189
Step 3: We consider the new divisor 287 and the new remainder 189, and apply the division lemma to get
287 = 189 x 1 + 98
We consider the new divisor 189 and the new remainder 98,and apply the division lemma to get
189 = 98 x 1 + 91
We consider the new divisor 98 and the new remainder 91,and apply the division lemma to get
98 = 91 x 1 + 7
We consider the new divisor 91 and the new remainder 7,and apply the division lemma to get
91 = 7 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 1337 and 6972 is 7
Notice that 7 = HCF(91,7) = HCF(98,91) = HCF(189,98) = HCF(287,189) = HCF(1337,287) = HCF(6972,1337) .
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Frequently Asked Questions on HCF of 1337, 6972 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 1337, 6972?
Answer: HCF of 1337, 6972 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1337, 6972 using Euclid's Algorithm?
Answer: For arbitrary numbers 1337, 6972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.