Highest Common Factor of 972, 759, 985 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, 759, 985 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 972, 759, 985 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, 759, 985 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, 759, 985 is 1.
HCF(972, 759, 985) = 1
HCF of 972, 759, 985 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, 759, 985 is 1.
Highest Common Factor of 972,759,985 is 1
Step 1: Since 972 > 759, we apply the division lemma to 972 and 759, to get
972 = 759 x 1 + 213
Step 2: Since the reminder 759 ≠ 0, we apply division lemma to 213 and 759, to get
759 = 213 x 3 + 120
Step 3: We consider the new divisor 213 and the new remainder 120, and apply the division lemma to get
213 = 120 x 1 + 93
We consider the new divisor 120 and the new remainder 93,and apply the division lemma to get
120 = 93 x 1 + 27
We consider the new divisor 93 and the new remainder 27,and apply the division lemma to get
93 = 27 x 3 + 12
We consider the new divisor 27 and the new remainder 12,and apply the division lemma to get
27 = 12 x 2 + 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 759 is 3
Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(93,27) = HCF(120,93) = HCF(213,120) = HCF(759,213) = HCF(972,759) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 985 > 3, we apply the division lemma to 985 and 3, to get
985 = 3 x 328 + 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 985 is 1
Notice that 1 = HCF(3,1) = HCF(985,3) .
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Frequently Asked Questions on HCF of 972, 759, 985 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, 759, 985?
Answer: HCF of 972, 759, 985 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 972, 759, 985 using Euclid's Algorithm?
Answer: For arbitrary numbers 972, 759, 985 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.