Highest Common Factor of 1974, 9502 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 1974, 9502 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1974, 9502 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 1974, 9502 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 1974, 9502 is 2.
HCF(1974, 9502) = 2
HCF of 1974, 9502 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1974, 9502 is 2.
Highest Common Factor of 1974,9502 is 2
Step 1: Since 9502 > 1974, we apply the division lemma to 9502 and 1974, to get
9502 = 1974 x 4 + 1606
Step 2: Since the reminder 1974 ≠ 0, we apply division lemma to 1606 and 1974, to get
1974 = 1606 x 1 + 368
Step 3: We consider the new divisor 1606 and the new remainder 368, and apply the division lemma to get
1606 = 368 x 4 + 134
We consider the new divisor 368 and the new remainder 134,and apply the division lemma to get
368 = 134 x 2 + 100
We consider the new divisor 134 and the new remainder 100,and apply the division lemma to get
134 = 100 x 1 + 34
We consider the new divisor 100 and the new remainder 34,and apply the division lemma to get
100 = 34 x 2 + 32
We consider the new divisor 34 and the new remainder 32,and apply the division lemma to get
34 = 32 x 1 + 2
We consider the new divisor 32 and the new remainder 2,and apply the division lemma to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1974 and 9502 is 2
Notice that 2 = HCF(32,2) = HCF(34,32) = HCF(100,34) = HCF(134,100) = HCF(368,134) = HCF(1606,368) = HCF(1974,1606) = HCF(9502,1974) .
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Frequently Asked Questions on HCF of 1974, 9502 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 1974, 9502?
Answer: HCF of 1974, 9502 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1974, 9502 using Euclid's Algorithm?
Answer: For arbitrary numbers 1974, 9502 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.