Highest Common Factor of 147, 974 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 147, 974 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 147, 974 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 147, 974 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 147, 974 is 1.
HCF(147, 974) = 1
HCF of 147, 974 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 147, 974 is 1.
Highest Common Factor of 147,974 is 1
Step 1: Since 974 > 147, we apply the division lemma to 974 and 147, to get
974 = 147 x 6 + 92
Step 2: Since the reminder 147 ≠ 0, we apply division lemma to 92 and 147, to get
147 = 92 x 1 + 55
Step 3: We consider the new divisor 92 and the new remainder 55, and apply the division lemma to get
92 = 55 x 1 + 37
We consider the new divisor 55 and the new remainder 37,and apply the division lemma to get
55 = 37 x 1 + 18
We consider the new divisor 37 and the new remainder 18,and apply the division lemma to get
37 = 18 x 2 + 1
We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get
18 = 1 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 147 and 974 is 1
Notice that 1 = HCF(18,1) = HCF(37,18) = HCF(55,37) = HCF(92,55) = HCF(147,92) = HCF(974,147) .
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Frequently Asked Questions on HCF of 147, 974 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 147, 974?
Answer: HCF of 147, 974 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 147, 974 using Euclid's Algorithm?
Answer: For arbitrary numbers 147, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.