Highest Common Factor of 598, 972, 648 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 598, 972, 648 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 598, 972, 648 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 598, 972, 648 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 598, 972, 648 is 2.
HCF(598, 972, 648) = 2
HCF of 598, 972, 648 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 598, 972, 648 is 2.
Highest Common Factor of 598,972,648 is 2
Step 1: Since 972 > 598, we apply the division lemma to 972 and 598, to get
972 = 598 x 1 + 374
Step 2: Since the reminder 598 ≠ 0, we apply division lemma to 374 and 598, to get
598 = 374 x 1 + 224
Step 3: We consider the new divisor 374 and the new remainder 224, and apply the division lemma to get
374 = 224 x 1 + 150
We consider the new divisor 224 and the new remainder 150,and apply the division lemma to get
224 = 150 x 1 + 74
We consider the new divisor 150 and the new remainder 74,and apply the division lemma to get
150 = 74 x 2 + 2
We consider the new divisor 74 and the new remainder 2,and apply the division lemma to get
74 = 2 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 598 and 972 is 2
Notice that 2 = HCF(74,2) = HCF(150,74) = HCF(224,150) = HCF(374,224) = HCF(598,374) = HCF(972,598) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 648 > 2, we apply the division lemma to 648 and 2, to get
648 = 2 x 324 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 648 is 2
Notice that 2 = HCF(648,2) .
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Frequently Asked Questions on HCF of 598, 972, 648 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 598, 972, 648?
Answer: HCF of 598, 972, 648 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 598, 972, 648 using Euclid's Algorithm?
Answer: For arbitrary numbers 598, 972, 648 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.