Highest Common Factor of 972, 987, 178 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 972, 987, 178 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 987, 178 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 972, 987, 178 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 972, 987, 178 is 1.
HCF(972, 987, 178) = 1
HCF of 972, 987, 178 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 972, 987, 178 is 1.
Highest Common Factor of 972,987,178 is 1
Step 1: Since 987 > 972, we apply the division lemma to 987 and 972, to get
987 = 972 x 1 + 15
Step 2: Since the reminder 972 ≠ 0, we apply division lemma to 15 and 972, to get
972 = 15 x 64 + 12
Step 3: We consider the new divisor 15 and the new remainder 12, and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 972 and 987 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(972,15) = HCF(987,972) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 178 > 3, we apply the division lemma to 178 and 3, to get
178 = 3 x 59 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 178 is 1
Notice that 1 = HCF(3,1) = HCF(178,3) .
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Frequently Asked Questions on HCF of 972, 987, 178 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 972, 987, 178?
Answer: HCF of 972, 987, 178 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 987, 178 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 987, 178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.